DSQ: Calculating the endpoints of a line segment - GMAT Quantitative Reasoning
Card 0 of 4
Consider segment 
with midpoint 
at the point 
.
I) Point 
has coordinates of 
.
II) Segment 
has a length of 
units.
What are the coordinates of point 
?
Consider segment
I) Point
II) Segment
What are the coordinates of point
In this case, we are given the midpoint of a line and asked to find one endpoint.
Statement I gives us the other endpoint. We can use this with midpoint formula (see below) to find our other point.
Midpoint formula: 
Statment II gives us the length of the line. However, we know nothing about its orientation or slope. Without some clue as to the steepness of the line, we cannot find the coordinates of its endpoints. You might think we can pull of something with distance formula, but there are going to be two unknowns and one equation, so we are out of luck.
So,
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
In this case, we are given the midpoint of a line and asked to find one endpoint.
Statement I gives us the other endpoint. We can use this with midpoint formula (see below) to find our other point.
Midpoint formula:
Statment II gives us the length of the line. However, we know nothing about its orientation or slope. Without some clue as to the steepness of the line, we cannot find the coordinates of its endpoints. You might think we can pull of something with distance formula, but there are going to be two unknowns and one equation, so we are out of luck.
So,
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
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Find endpoint 
given the following:
I) Segment 
has its midpoint at 
.
II) Point 
is located on the 
-axis, 
points from the origin.
Find endpoint
I) Segment
II) Point
Find endpoint Y given the following:
I) Segment RY has its midpoint at (45,65)
II) Point R is located on the x-axis, 13 points from the origin.
I) Gives us the location of the midpoint of our segment
(45,65)
II) Gives us the location of one endpoint
(13,0)
Use I) and II) to work backwards with midpoint formula to find the other endpoint.
So endpoint 
is at 
.
Therefore, both statements are needed to answer the question.
Find endpoint Y given the following:
I) Segment RY has its midpoint at (45,65)
II) Point R is located on the x-axis, 13 points from the origin.
I) Gives us the location of the midpoint of our segment
(45,65)
II) Gives us the location of one endpoint
(13,0)
Use I) and II) to work backwards with midpoint formula to find the other endpoint.
So endpoint
Therefore, both statements are needed to answer the question.
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Consider segment 
I) Endpoint 
is located at the origin
II) 
has a distance of 36 units
Where is endpoint 
located?
Consider segment
I) Endpoint
II)
Where is endpoint
To find the endpoint of a segment, we can generally use the midpoint formula; however, in this case we do not have enough information.
I) Gives us one endpoint
II) Gives us the length of DF
The problem is that we don't know the orientation of DF. It could go in infinitely many directions, so we can't find the location of 
without more information.
To find the endpoint of a segment, we can generally use the midpoint formula; however, in this case we do not have enough information.
I) Gives us one endpoint
II) Gives us the length of DF
The problem is that we don't know the orientation of DF. It could go in infinitely many directions, so we can't find the location of
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is the midpoint of line PQ. What are the coordinates of point P?
(1) Point Q is the origin.
(2) Line PQ is 8 units long.
(1) Point Q is the origin.
(2) Line PQ is 8 units long.
The midpoint formula is
,
with statement 1, we know that Q is 
and can solve for P:
and 
Statement 1 alone is sufficient.
Statement 2 doesn't provide enough information to solve for point P.
The midpoint formula is
with statement 1, we know that Q is
Statement 1 alone is sufficient.
Statement 2 doesn't provide enough information to solve for point P.
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